Hierarchical Geometric Cluster Detection

This work describes a general method for the detection of affine structures in a set of elements that belong to a certain ambient space. The general idea is that such structures express themselves as unusual concentrations of subsets of such elements around these structures, as opposed to being randomly scattered throughout the space. Whereas existing detection methods assume a global uniform point process over the whole data range as the background model, our method constructs a local background model in the vicinity of the structure, which enables a more precise and versatile detection scheme.
Since the size (scale) of the local analysis region is a key element in the detection, we develop a multi-scale extension of the aforementioned idea. The results are shown on various synthetic datasets.